188 



REASONING. 



them. Every valid ratiocination, therefore, may be stated in 



the first figure, that is, in one of the following forms : 

 Every B is C No B is C 



AHA ) -n AHA ) -p 



Some A } B ' Some A J 1B B ' 



therefore therefore 



All A ] is c. No A is 



Some A j Some A is not 



Or if more significant symbols are preferred : 



To prove an affirmative, the argument must admit of being 



stated in this form : 



All animals are mortal ; 



All men \ 



Some men [ are animals ; 



Socrates ; 



therefore 

 All men \ 



Some men Y are mortal. 

 Socrates J 



To prove a negative, the argument must be capable of being 

 expressed in this form : 



No one who is capable of self-control is necessarily 

 vicious ; 



All negroes \ 



Some negroes are capable of self-control; 



Mr. A's negro ) 



therefore 



No negroes are \ 



Some negroes are not [ necessarily vicious. 



Mr. A's negro is not J 



Though all ratiocination admits of being thrown into one 

 or the other of these forms, and sometimes gains consider- 

 ably by the transformation, both in clearness and in the 

 obviousness of its consequence ; there are, no doubt, cases 

 in which the argument falls more naturally into one of the 

 other three figures, and in which its conclusiveness is more 



